1: Field of the Invention
The present invention relates generally to the field of x-ray interactions with matter and, more particularly, to methods for scattering, filtering and attenuating x-rays.
2: Background on X-Ray Absorption and Scattering
It is often desirable to attenuate x-ray beams. This is commonly done by filtering or scattering methods, which strongly depend upon the x-rays' energy and so alter the spectrum of the incident beam, often drastically. In many cases this is not a serious problem. But in certain cases involving instrumentation calibration procedures, the incident spectrum is precisely the quantity of interest yet attenuation is required because the incident intensity is too high for the measuring instrument. An example is calibrating an x-ray mammography machine using a solid state spectrometer. In these cases it would be beneficial to have a method to reduce intensity without introducing significant amounts of spectral distortion.
In the following sections the interactions between x-rays and matter are briefly described, both because they represent prior art and are relevant to an understanding of the present invention. For x-ray energies below 1.2 MeV, where pair production becomes possible, the three primary mechanisms by which x-rays interact with matter are through its electrons by elastic or Raleigh scattering; Compton scattering; and photoelectric absorption. These processes have been much studied and extensive details may be found in such texts as Warren, B. E., "X-ray Diffraction" (Addison-Wesley, Menlo Park, Calif., 1969), James, R. W., "The Optical Principles of the Diffraction of X-rays" (Oxbow Press, Woodbridge, Conn., 1982), Guinier, A., "X-ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies" (W. H. Freeman, San Francisco, 1963), and Heitler, W., "The Quantum Theory of Radiation", 3.sup.rd. ed. (Oxford University Press, Oxford, 1954).
2.1 Photoelectric Absorption
In photoelectric absorption, an atom absorbs an x-ray and ejects an electron, the photoelectron. For an electron in quantum state i, photoelectron absorption can occur only when the energy of the x-ray, E, exceeds the binding energy E.sub.i of the state i. The photoelectric cross section .sigma..sub.A (E) depends strongly on both the atom's atomic number Z (.about.Z.sup.4) and the energy difference (.about.(E-Ei).sup.-3). FIG. 1 shows the photoelectric absorption cross section .sigma..sub.A (E) in iron (Fe) 2, which is seen to vary by several orders of magnitude as a function of x-ray energy E. The fraction A(t,E) of x-rays absorbed in a piece of material of thickness t is given by: EQU A(t,E)=1-exp(-t .mu..sub.A (E)), (1)
where .mu..sub.A (E) is the photoelectric absorption coefficient in inverse cm. 1/.mu..sub.A (E) is called the absorption length. Using Eqn. 1 and the data of FIG. 1, one can calculate that at 10 keV, for example, only 4 microns of Fe are required to provide 99.9% absorption, whereas at 40 keV 204 microns are required. This strong energy dependence is typical of photoelectric absorption.
2.2 Compton Scattering
In Compton scattering the x-ray photon scatters inelastically from a single electron, transferring momentum and energy to it in the process. FIG. 1 also shows the Compton scattering cross section .sigma..sub.C (E.sub.x) 3 in Fe. This component becomes the dominant energy loss mechanism by about 110 keV. As may be seen, its energy dependence is much slower than that of photoelectron absorption. The general theory of Compton scattering is quite complex, particularly if such issues as x-ray polarization, electron spin and momentum, relativistic terms, and many body interactions are included. [See, for example, Platzman, P. & Tzoar, N., "Theory", Chapter 2 in Compton Scattering, ed. B. Williams (McGraw-Hill, New York, 1977).] The present invention, however, may be understood by reference to a simple kinematical description of the x-ray energy loss .DELTA.E.sub.C in Compton scattering, ignoring x-ray polarization effects: EQU .DELTA.E.sub.C =E(1-[1+.alpha.(1-cos .theta.)].sup.-1) (2)
for scattering angle .theta. where .alpha.=E/m.sub.e c.sup.2 =E/511 keV, m.sub.e is the rest mass of the electron and c is the speed of light.
2.3 Elastic Scattering
In elastic scattering the x-ray does not lose energy but exchanges momentum with electrons by electric field interactions. The details of this process are complex, both because of resonances which can occur when the energy of the x-ray is near to an atomic absorption edge and also because of interference phenomena which occur if the locations of either the electrons (e.g. in atoms) or the atoms they are attached to (e.g. in crystals) are correlated. The differential scattering cross section for elastic scattering for unpolarized x-rays at momentum transfer x is commonly expressed as EQU d.sigma..sub.E /d.OMEGA.=0.5r.sup.2.sub.e (1+cos.sup.2 .theta.)FF(x),(3)
where r.sub.e =2.82.times.10.sup.-13 cm is the classical electron radius, and x is related to the energy E.sub.x and scattering angle .theta. by EQU x=(E/hc)sin(.theta./2), (4)
where hc=12.4 keV-A.degree.. The form factor FF(x) expresses interference effects in the scattering process, being essentially the Fourier transform of the scatter's electron density function. For crystalline materials FF(x) can be computed, for non-crystalline materials it must be measured. It is important to note that x-rays of different energy can transfer the same momentum value x by scattering at different angles .theta.. FIG. 1. also shows the elastic scattering cross section .sigma..sub.E (E) 5 in Fe. As shown, .sigma..sub.E (E) varies more strongly with x-ray energy E than .sigma..sub.C (E) but not so strongly as .sigma..sub.PE (E).
3: Brief Survey of Existing Art
The field of x-ray detection is highly developed. A fairly comprehensive introduction to the state of the art may be found in the volume "Radiation Detection and Measurement, 2.sup.nd Ed." by Glenn F. Knoll (J. Wiley, New York, 1989). However, when one wishes to determine the energy spectrum of a source, there are basically three common approaches plus one proprietary method.
3.1 Bragg Scattering Approaches
The first common approach is to use a Bragg diffracting crystal scattering at angle 2.theta. to measure the source flux at a single energy E(.theta.) given by the Bragg condition EQU E(.theta.)=nhc/(2d sin(.theta.)). (5)
The measurement is repeated for as many .theta. values as desired, allowing the source spectrum to be mapped out. While this approach has excellent energy resolution, it is extremely tedious due to the number of measurements which must be made. In a variation of this approach, Deslattes (U.S. Pat. No. 5,381,458) used a curved crystal to diffract an entire spectrum onto a linear detector simultaneously. While this approach is fast, the instrument itself is often too bulky, difficult to align, and fragile for routine applications.
3.2 Energy Dispersive Detectors
The second common approach is to use solid state, energy dispersive detectors. These devices have poorer energy resolution than the foregoing (100s of eV rather than eV) but it is often adequate for calibration purposes and they are capable of acquiring a complete spectrum at once. Their major limitation for measuring sources is their limited count rate capability, typically less than 200,000 counts/sec. By comparison, a typical mammography source produces approximately 10.sup.8 x-rays/sec/mm.sup.2 at its working distance of 60 cm. As a result, the only way solid state detectors can be used to calibrate sources is at long measurement distances, using the 1/r.sup.2 law to attenuate the source. Since these distances can be considerable (10's of meters) and the flight paths must be evacuated, this approach is not suitable for routine measurements.
3.3 Source Filtering
The third common approach has been to measure the source through a set of two or more filters, either sequentially with the same detector or in parallel with multiple detectors. (See as examples U.S. Pat. Nos. 4,935,950, 4,697,280, 4,189,645, and 4,355,230.) These systems can typically measure only a single or small number of characteristics of the source spectrum, for example its high energy cutoff (kVp value) or a weighted mean energy (e.g. half value layer) unless a very large number of filters is used. Even so, attainable energy resolution is very poor, perhaps a few keV. The following brief example will clarify the problems which arise when an x-ray source is attenuated by filtering and/or scattering.
FIG. 2A shows the output spectrum from a molybdenum (Mo) x-ray tube, 7 in a typical mammography machine, as calculated from the semiempirical model of Tucker et al. "Molybdenum target x-ray spectra: A semiempirical model", Medical Physics, Vol. 18, pp. 402-407 (1991) for an exposure of 200 mAs and a peak excitation voltage, kV.sub.p, of 30 kV. At 60 cm, this system delivers about 1.2.times.10.sup.8 photons/sec into a 1 mm.sup.2 area, which is more than 1000 times the rate capability of a high speed solid state detector. We have attempted reducing the total count rate using a 50 .mu.m pinhole, but discovered two problems. First the 40/1 aspect ratio of the "pinhole" in 2 mm Ta made it difficult to reliably align pointing toward the source. Second, the high local flux density was found to cause electrical damage in the contacts to some of our x-ray detectors.
FIG. 2B shows the effect of reducing the spectrum's intensity 1000-fold by attenuation through a 385 .mu.m Fe foil. As may be seen, the entire spectrum 8 is hugely distorted, with the low energy end attenuated beyond recovery.
FIG. 2C shows the effect of attenuating the spectrum by scattering at 90.degree. 9 from a piece of iron into a 0.01 steradian solid angle. The small solid angle was chosen to minimize the variance in Compton energy loss with scattering angle. This approach has several problems. First, the elastic scattering has the Compton scattering overlaid on it on a shifted energy and non-linear energy scale, giving two pairs of lines, etc. Second, the scattering is too weak from the modeled solid acceptance angle: the flux is reduced by 10.sup.5. Third, the spectrum is still considerably distorted by the energy dependencies of both scattering processes. Further, if a larger solid angle were used to get more flux, then the Compton spectrum would become considerably smeared by the range of allowed scattering angles and Fe fluorescence from the foil would also become important, introducing spurious K-line peaks into the spectrum near 6 keV.
These figures therefore illustrate the typical problems encountered when scattering or attenuation are used to reduce x-ray intensity.
3.4 A Proprietary Compton Scattering Approach
RTI Electronics AB of Sweden has produced an instrument using the method of FIG. 2C with a low Z scatterer. The details of the method have been published by Matscheko and Ribberfors in Physics Medical Biology, Vol. 34, pp. 835-841 (1989) and Vol. 32, pp. 577-594 (1987). A tiny range of scattering angles centered about 90.degree. is used between the source and an energy dispersive detector. Since the energy loss on Compton scattering at a fixed angle is given by Eqn. 2, then, given a very small range of scattering angles, they can mathematically reconstruct the original spectrum from the observed spectrum. The necessarily small range of acceptance angles means that it requires 20 seconds or more to acquire a spectrum, which can exceed the allowable on-times for high power x-ray tubes. The commercial apparatus, with its carefully aligned collimators, is also bulky and expensive.
3.5 Synopsis
From the foregoing it is clear that, in many applications, it would be quite advantageous if x-ray beams could be attenuated by several orders of magnitude without introducing significant spectral distortion. The availability of such an attenuator would then allow solid state detectors to be used effectively in source spectral measurements and facilitate the development of compact portable instruments for calibrating x-ray sources in medical application such as mammography and elsewhere.